It is a federal law for felons not to have either for a host of reasons.
FEDERAL AMMUNITION LAW
Miscellaneous Restrictions
Federal law prohibits ammunition sale or transfer to, and possession by, anyone who:
1. is under indictment for a crime punishable by more than one year imprisonment or convicted of a felony,
2. is a fugitive from justice,
3. is an unlawful user of a controlled substance,
4. is addicted to a controlled substance,
5. has been adjudicated as a mental defective or committed to a mental institution,
6. is an illegal alien,
7. has been dishonorably discharged from the military, and
8. has renounced his or her U.S. citizenship (18 USC § 922(d) and (g)).
Subjects of Domestic Violence Restraining Orders
Federal law also prohibits anyone from transporting, receiving, or possessing ammunition if he is the subject of a domestic violence order restraining him from harassing, stalking, or threatening an intimate partner or the partner's child. The subject of the order is barred from purchasing firearms or ammunition if a judge (or other hearing officer) determines that the subject poses a credible threat to the physical safety of the intimate partner or child (18 USC § 922(d)(8)B)). Before making this determination, the court or officer must give the person a hearing opportunity.
The law also prohibits anyone convicted of a misdemeanor domestic violence crime from purchasing or possessing ammunition (18 USC § 922(d) and (g)).
Minimum Age Restrictions
Federal law regulates the sale of ammunition to young people. It bars licensed manufacturers or dealers from selling long gun ammunition to anyone who they believe is under age 18. Also they may not sell handgun ammunition to anyone they reasonably believe is under age 21 (18 USC § 922(b)(1)).
http://www.cga.ct.gov/2007/rpt/2007-R-0217.htm